I remember seeing pictures of this as a kid and wondered whether anyone has since recreated this saucer-wing aircraft and made it work?
Source (excuse the pun)
I'm not aware of anyone making a replica of the Sack AS-6 (the aircraft was destroyed when the Allies reached the area); however, there are other examples of saucer (circular wing)- like the Rowe UFO, which flies quite happily.
Rowe UFO; image from youtube grab
Then there is also the Vought V-173, whose design is quite similar.
Vought V-173 By Unknown - http://www.flickr.com/photos/sdasmarchives/4822056685/, Public Domain, Link
Well there was the Vought XFV-173 'Flying Pancake'.
These were the first experimental lifting body designs and the technology demonstrator for the Vought XF5U naval fighter. It boasted exceptional performance for a propeller powered aircraft but was obsolete by the time it would have entered service in the advent of jets.
Saucer shaped aircraft have been explored from time to time. Everything from exotic concept studies like this proposed Mach 4 saucer craft manufactured by Avro Canada to real prototypes like the VZ-9 AvroCar.
It is possible that said designs or other as-yet declassified aircraft have given the public the (false) impression that the government is reverse engineering extraterrestrial craft designed and built by EBEs.
See the ancestor of most of these. A more "normal" airplane of the extremely low-aspect-ratio sort than the Vought/Zimmerman digression into VTOL. The most useful in-practice planes of such a sort with any operational history. (though the V-173 also flew many pilots and hours) ("Air-Up") South Bend, Indiana. Arup S-2 first flew in '32. It and the S-4 between the two planes flew airshows for multiple seasons, multiple pilots including 2 novices. They apparently flew on until age of the airframe retired them, carrying advertizing to pay for shop and hangar space. S-2 was ~900 lbs and flew 84kts on 37 horsepower. S-4 was dual-control 2 seat,all-up ~1400 bs,; flew 99kts on 70hp. Landing speeds ~20mph, with steep climb-out and approach. Stall and spin-proof. Existing video (youtubes) shows them being nimble and quick, not risky or tricky.
S-2 flew for NACA & the Army & the CAA and Charles Zimmerman was on the NACA team that saw the amazing performance it put on, and after that, came up with the planform that grew into the V-173, when he went to work for Vought. The Arup planes and the Nemeth show that it did not need the exaggerated outward-turning props for lift or control or low-speed ability or efficiency. NACA tunnel tests with powered models showed no substantial improvement over the props turning the other direction ("inwards at the tip"). Slight loss of stability & control in low-speed extremely high AoA flight, with the props outward-turning. Yet they progressed with the exploration of using tuned-length & speed props to direct the airflow in various ways.
Another "plane for everyone" of the sort was the '34 Nemeth "parachute plane", with a circular wing parasol above a normal Argo biplane fuselage. Faster than the original, with amazing slow and STOL performance and stall/spin proof.
As with the Arup planes, no-one showed any interest in it commercially. "Conventional wisdom" seems to say they couldn't fly, or not well and they're just silly toys anyway even if they can).
Any number of things could stop the Sack plane from working, even if the Arup & the Nemeth, the Rowe & the Hatfield "Little Bird" work just fine. CG, pitch, AoA, balance or airfoil could stop it. The first "Little Bird" had too much reflex & anhedral and was either very good at being very fast or very slow and tricky in between. Later iterations provided the cure, & it was "ideal" at re-creating the qualities of the Arup.
It's not known how well the Rowe UFO flies, just that it does, and seems normal. Is there strong reason to doubt. Models of such things are ridiculously maneuverable (they hover with a single prop, not needing the twin-outward-turning props). It's not known how a man-sized plane that had more horsepower and could pull Gs would maneuver.